Nesscliffe can be done, and it's probably the closest and cheapest good place to go. Train to shrewsbury then a bus to the crag.
I'm pretty sure Pontesford is do-able as well, train to shrewsbury then bus, although i don't know the details. There's fair few routes to do there from mod into the low e's, you can definatly spend a good day there. And it was in fact Partly developed by the club back in the day!
You could also have a look in the West Midlands guidebook for idea's of were to go. Some of it's free from here (Including pontesford rocks)
http://westmidlandsrock.co.uk/ the club also has a copy.
Rosie and I went to the Malvern hills in our first year and that was really cheap to get to, a fiver return on the train i think, but It was raining and dirty and i took a bit of a fall, luckily I caught a tree on the way down, it scared Rosie though
It wasn't a particularly inspiring place to go, but maybe that's just because it was raining...